Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5, 6, 7, 8	,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
2	reference	9	⊢
3	instantiation	48	⊢
	: , :
4	instantiation	14, 9	⊢
	:
5	reference	11	⊢
6	instantiation	48	⊢
	: , :
7	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
8	instantiation	10, 11, 12, 13	,  ⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
10	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
11	instantiation	14, 15	⊢
	:
12	instantiation	16, 17, 18	,  ⊢
	: , :
13	instantiation	19, 76, 62	,  ⊢
	: , :
14	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
15	instantiation	20, 74, 71	⊢
	: , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
17	instantiation	77, 52, 21	⊢
	: , : , :
18	instantiation	29, 22, 23	,  ⊢
	: , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
20	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
21	instantiation	77, 57, 24	⊢
	: , : , :
22	instantiation	45, 32, 25	,  ⊢
	: , :
23	instantiation	26, 27, 28	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
25	instantiation	29, 30, 31	,  ⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	37, 79, 33, 38, 35, 39, 32, 46, 47, 41	,  ⊢
	: , : , : , : , : , :
28	instantiation	37, 38, 74, 33, 39, 34, 35, 42, 43, 46, 47, 41	,  ⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	45, 36, 41	,  ⊢
	: , :
31	instantiation	37, 38, 74, 79, 39, 40, 46, 47, 41	,  ⊢
	: , : , : , : , : , :
32	instantiation	45, 42, 43	⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
34	instantiation	48	⊢
	: , :
35	instantiation	44	⊢
	: , : , :
36	instantiation	45, 46, 47	⊢
	: , :
37	theorem		⊢
	proveit.numbers.multiplication.disassociation
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	48	⊢
	: , :
41	instantiation	77, 52, 49	,  ⊢
	: , : , :
42	instantiation	77, 52, 50	⊢
	: , : , :
43	instantiation	77, 52, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
45	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
47	instantiation	77, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49	instantiation	77, 55, 54	,  ⊢
	: , : , :
50	instantiation	77, 55, 56	⊢
	: , : , :
51	instantiation	77, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
54	instantiation	77, 60, 59	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	77, 60, 70	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
59	instantiation	77, 61, 62	,  ⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	63, 64, 65	⊢
	: , :
62	assumption		⊢
63	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
64	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
65	instantiation	66, 67, 68	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	69, 70, 71	⊢
	: , :
68	instantiation	72, 73	⊢
	:
69	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
70	instantiation	77, 78, 74	⊢
	: , : , :
71	instantiation	77, 75, 76	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.negation.int_closure
73	instantiation	77, 78, 79	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
76	assumption		⊢
77	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat1